The assertions of Proposition 3.7 in our paper ``The robust superreplication problem: A dynamic approach"" [L. Carassus, J. Ob\lo'\j, and J. Wiesel, SIAM J. Financial Math., 10 (2019), pp. 907--941] may ...
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The assertions of Proposition 3.7 in our paper ``The robust superreplication problem: A dynamic approach"" [L. Carassus, J. Ob\lo'\j, and J. Wiesel, SIAM J. Financial Math., 10 (2019), pp. 907--941] may fail to hold without an additional assumption, which we detail in this erratum.
We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a z...
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We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamicprogramming approach for stochastic optimal control and derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies. (c) 2012 Elsevier B.V. All rights reserved.
Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network perfo...
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Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network performance and network costs simultaneously. In this paper we need to carefully look into how well the concept of shortest disjoint paths is incorporated for given objective functions. Seven objective functions and four algorithms are presented to evaluate the concept of k-shortest disjoint paths for the design of a robust WDM optical network. A case study based on simulation experiments is conducted to illustrate the application and efficiency of k-shortest disjoint paths in terms of following objective goals: minimal wavelengths, minimal wavelength link distance, minimal wavelength mileage costs, even distribution of traffic flows, average restoration time of backup lightpaths, and physical topology constraints.
An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using...
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An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability. (C) 2016 Elsevier B.V. All rights reserved.
We consider a deterministic optimal control problem, focusing on a finite horizon scenario. Our proposal involves employing deep neural network approximations to capture Bellman's dynamic programming principle. Th...
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We consider a deterministic optimal control problem, focusing on a finite horizon scenario. Our proposal involves employing deep neural network approximations to capture Bellman's dynamic programming principle. This also corresponds to solving first-order Hamilton-Jacobi-Bellman (HJB) equations. Our work builds upon the research conducted by Hur & eacute;et al. (SIAM J Numer Anal 59(1):525-557, 2021), which primarily focused on stochastic contexts. However, our objective is to develop a completely novel approach specifically designed to address error propagation in the absence of diffusion in the dynamics of the system. Our analysis provides precise error estimates in terms of an average norm. Furthermore, we provide several academic numerical examples that pertain to front propagation models incorporating obstacle constraints, demonstrating the effectiveness of our approach for systems with moderate dimensions (e.g., ranging from 2 to 8) and for nonsmooth value functions.
Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since ...
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Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since the discretizations typically suffer from the curse of dimensionality. In this paper we introduce a novel approximation technique for the value function of an infinite horizon optimal control. The method is based on solving optimal open loop control problems on a finite horizon with a sampling of the global value function along the generated trajectories. For the interpolation we choose a kernel orthogonal greedy strategy, because these methods are able to produce extreme sparse surrogates and enable rapid evaluations in high dimensions. Two numerical examples prove the performance of the approach and show that the method is able to deal with high-dimensional feedback control problems, where the dimensionality prevents the approximation by most existing methods. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
In this paper, we study a the specific Hyperbolic Absolute Risk Aversion (HARA) case of corporate international optimal Portfolio and consumption choice problem. The investor can invest his wealth bond (bank account)....
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ISBN:
(纸本)9787900719706
In this paper, we study a the specific Hyperbolic Absolute Risk Aversion (HARA) case of corporate international optimal Portfolio and consumption choice problem. The investor can invest his wealth bond (bank account). On the other hand, he can invest his money to a real project with production in a foreign country. Using the celebrated dynamical programmingprinciple method we provide the explicit optimal investment and consumption solution and give some simulation results to illustrates the influence of the volatility parameters on the optimal choice.
In this paper, we consider an insurance company that is active in multiple dependent lines. We assume that the risk process in each line is a Cramer-Lundberg process. We use a common shock dependency structure to cons...
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In this paper, we consider an insurance company that is active in multiple dependent lines. We assume that the risk process in each line is a Cramer-Lundberg process. We use a common shock dependency structure to consider the possibility of simultaneous claims in different lines. According to a vector of reinsurance strategies, the insurer transfers some part of its risk to a reinsurance company. Our goal is to maximize our objective function (expected discounted surplus level integrated over time) using a dynamicprogramming method. The optimal objective function (value function) is characterized as the unique solution of the corresponding Hamilton-Jacobi-Bellman equation with some boundary conditions. Moreover, an algorithm is proposed to numerically obtain the optimal solution of the objective function, which corresponds to the optimal reinsurance strategies.
In this work we propose a stochastic model for a sequencing-batch reactor (SBR) and for a chemostat. Both models are described by systems of Stochastic Differential Equations (SDEs), which are obtained as limits of su...
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In this work we propose a stochastic model for a sequencing-batch reactor (SBR) and for a chemostat. Both models are described by systems of Stochastic Differential Equations (SDEs), which are obtained as limits of suitable Markov Processes characterizing the microscopic behavior. We study the existence of solutions of the obtained equations as well as some properties, among which the possible extinction of the biomass is the most remarkable feature. The implications of this behavior are illustrated in the problem consisting in maximizing the probability of reaching a desired depollution level prior to biomass extinction. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
This paper is concerned with a kind of optimal portfolio and consumption choice problem, where an investor can invest his wealth in a trade project and foreign exchange deposit. The trade project earns profit by buyin...
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ISBN:
(纸本)9789881563972
This paper is concerned with a kind of optimal portfolio and consumption choice problem, where an investor can invest his wealth in a trade project and foreign exchange deposit. The trade project earns profit by buying the merchandise and selling it with a higher price. The bank pays at an interest rate for any deposit, and vice takes at a large rate for any loan. The optimal strategy is obtained by Hamilton-Jacobi-Bellman (HJB) equation, which is derived from dynamic programming principle. For the specific Hyperbolic Absolute Risk Aversion (HARA) case, we get the explicit form of optimal portfolio and consumption solution, and we give some simulation results.
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